Roscoe must play 9 commercials during his 1-hr radio show. Each commercial is either thirty seconds or sixty seconds long. If the total commercial time during that hour is 6 minutes, how many commercials of each type does Roscoe play?
Round answers to the nearest whole number.
___thirty second commercials
___sixty second commercials
To solve this problem, let's assign variables to the number of commercials. Let's call the number of thirty-second commercials "x" and the number of sixty-second commercials "y".
According to the problem, Roscoe must play a total of 9 commercials. So we can write the equation:
x + y = 9 (Equation 1)
We also know that the total commercial time during the hour is 6 minutes, which can be written as 6 x 60 = 360 seconds. Since each thirty-second commercial adds 30 seconds and each sixty-second commercial adds 60 seconds, the total commercial time can also be expressed as:
30x + 60y = 360 (Equation 2)
Now we have a system of two equations (Equation 1 and Equation 2) that we can solve simultaneously to find the values of x and y.
Let's solve Equation 1 for x:
x = 9 - y
Substitute this value of x into Equation 2:
30(9 - y) + 60y = 360
270 - 30y + 60y = 360
Combine the y-terms:
30y = 360 - 270
30y = 90
Divide both sides by 30:
y = 3
Substitute this value of y back into Equation 1 to solve for x:
x = 9 - 3
x = 6
Therefore, Roscoe must play 6 thirty-second commercials and 3 sixty-second commercials.
30x+60y=360
x+y=9